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Question 3. Let L be the language L = {we {a, b]* : w does NOT contain aba as a substring}. a. Draw the transition graph for an NFA that accepts L and has just one accept statc. b. By reducing the number of states in that NFA, find a regular expression that denotes the language L.Calculate the probability density | 4 100(r,0,$)| of finding the electron at the nucleus (considered as a point at the center of coordinates) for a hydrogen atom in the state 100. R10(r) = 2 Z 3/2 e-p/2 , Yoo(0,$) = - 2Zr (hbar)2 do p = nao mee2 Please notice that the above formulas are written in the cgs system of units, so mass is in grams, distance is in cm, and energy is in erg = g cm2/s2. In this system of units e = 4.8032068 X 10-statC, where 1 statC = 1 cm3/2 g1/2 s-1. O a. 0.18 pm-3 O b. 2.15 x 10-6 pm-3 O C. 1.54 x 10-18 pm-3 O d. 6.22 x 10-10 pm-3 O . 1.23 x 104 pm-34. (10 pts.) Consider the apparatus shown below which can be used to accelerate electrons. A potential difference AV is maintained between a cathode C and a plate anode A. A P Figure 1: Figure for problem 4 By definition, the electric field E at a point is the force on a unit charge at the point, and the potential function V is the related to the electric field as: E = -VV A free electron of charge e in the field will be accelerated toward A by a force: F = -EVV Compute the velocity of an electron accelerated from rest through a potential drop of 100,000 volts. The mass of an electron is 9.le-28 grams and it has a charge of -1.Ge-19 coulombs (C) or -4.8e-10 statcoulombs (statC). 1 statcoulomb or 1 electrostatic unit of charge (esu) = cm32g1/2g-1. 1 C = 329 statC.1) (10 Pts) Using the minimized DFA, use Arden's Lemma, or state removal algorithm to get regular expression corresponding to the language accepted by the machine. Initial state = 0 , Final states = {3} b 3 2